Asymptotically exact solution of the dynamic structure factor of an electron gas atrs≊3.5

An analytic expression for the dynamic structure factor S(k,ω) of a 3D electron gas is obtained by the recurrence relation method. It is valid for one metallic density ${\mathit{r}}_{\mathit{s}}$≊3.5 and is exact asymptotically, i.e., k≫${\mathit{k}}_{\mathit{F}}$ (${\mathit{k}}_{\mathit{F}}$ the Fermi wave vector). The result is based on an assumption, justified by the kinetic-energy and static-structure-factor sum rules and also numerically approximately corroborated. The expression is compared with an experimental measurement of Li at k=2.08${\mathit{k}}_{\mathit{F}}$.